Simple interest on a certain sum of money for 3 years at 8% per annum is equal to half of the compound interest on Rs. 16,000 for 2 years at 10% per annum. What is the principal sum that was placed on simple interest?

Introduction / Context:
This question connects two different interest situations: simple interest on an unknown principal and compound interest on a known sum. The simple interest for 3 years at 8% per annum is half of the compound interest on Rs. 16,000 for 2 years at 10% per annum. You must carefully compute the compound interest first, then relate it to the simple interest to find the unknown principal.

Given Data / Assumptions:
- Simple interest is on an unknown principal P at 8% per annum for 3 years.
- Compound interest is on Rs. 16,000 at 10% per annum for 2 years, compounded annually.
- S.I. for 3 years at 8% = ½ × C.I. for 2 years at 10% on Rs. 16,000.
- We must find P, the sum placed on simple interest.

Concept / Approach:
The approach is in two stages:
1) Calculate the compound interest on Rs. 16,000 for 2 years at 10%.
2) Take half of that amount to get the simple interest on P for 3 years at 8%.
Then, using the simple interest formula S.I. = P * R * T / 100, we can solve for P. This illustrates the interplay between C.I. and S.I. in exam problems.

Step-by-Step Solution:
Step 1: Compute compound amount on Rs. 16,000 at 10% for 2 years.Step 2: A = 16000 * (1.10)^2 = 16000 * 1.21 = 19360.Step 3: Compound interest on Rs. 16,000 = 19360 - 16000 = Rs. 3360.Step 4: Given that S.I. = half of this C.I. = 3360 / 2 = Rs. 1680.Step 5: Simple interest formula: 1680 = P * 8 * 3 / 100.Step 6: Simplify: 1680 = P * 24 / 100 = 0.24P.Step 7: Solve for P: P = 1680 / 0.24 = 7000.Step 8: Hence, the sum placed on simple interest is Rs. 7000.

Verification / Alternative check:
Check S.I. on Rs. 7000 at 8% for 3 years: S.I. = 7000 * 8 * 3 / 100 = 7000 * 24 / 100 = 1680. Half of C.I. on Rs. 16,000 (which we calculated as 3360) is also 1680, so the condition is satisfied exactly.

Why Other Options Are Wrong:
Rs. 14,000 would give S.I. of 3360, which equals full C.I., not half. Rs. 3,500, Rs. 5,600 and Rs. 9,000 give simple interest values that do not match 1680. They arise from misusing the factor ½ or from arithmetic errors in computing the compound interest.

Common Pitfalls:
Some students forget that the relationship is “half the compound interest”, not equal to it, and set S.I. = C.I. Others miscalculate the compound amount on Rs. 16,000 or mistakenly treat it as simple interest. Always compute the compound interest carefully, then apply the proportion given in the problem.

Final Answer:
The principal placed on simple interest is Rs. 7,000.